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Visible  and  Infra-Red  Radiation 
of  Hydrogen 


.11  rw  23  1926 


DISSERTATION 

SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES  OF  THE  JOHNS  HOPKINS 

UNIVERSITY  IN  CONFORMITY  WITH  THE  REQUIREMENTS  FOR  THE 

DEGREE  OF  DOCTOR  OF  PHILOSOPHY 


BY 


FREDERICK  SUMMER  BRACKETT 


// 

DMIY 


BALTIMORE 
1922 


Visible  and  Infra-Red  Radiation 
of  Hydrogen 


DISSERTATION 

SUBMITTED  TO  THE  BOARD  OF  UNIVERSITY  STUDIES  OF  THE  JOHNS  HOPKINS 

UNIVERSITY  IN  CONFORMITY  WITH  THE  REQUIREMENTS  FOR  THE 

DEGREE  OF  DOCTOR  OF  PHILOSOPHY 


BALTIMORE 
1922 


&C457 


VISIBLE  AND  INFRA-RED  RADIATION 
OF  HYDROGEN 

BY  FREDERICK  SUMNER  BRACKETT 

ABSTRACT 

Infra-red  spectrum  of  hydrogen  to  4.5  /«. — The  radiation  from  the  central  section 
of  a  long  discharge  tube,  such  as  the  one  used  by  Wood  to  extend  the  Balmer  series 
to  the  twentieth  term,  was  analyzed  by  means  of  a  rock-salt  prism  spectrometer,  and 
readings  were  taken  with  an  extremely  sensitive  vacuum  thermo-junction.  Besides 
some  unidentified  lines  (Fig.  i),  five  members  of  the  Paschen  series,  three  of  them 
new,  were  observed  at  the  wave-lengths  corresponding  to  the  formula  v  =  N(i/3*  — 
i/m2),  where  m  =  4,  5,  6,  7,  8;  also  the  first  two  members  of  a  new  series  corresponding 
to  v  =  N(i/4*—  i/w2),  where  #1  =  5,  6,  were  observed  at  4.05  and  2.63^.  According 
to  the  Bohr  theory  these  two  series  are  due  to  electrons  falling  from  outer  orbits  into 
the  third  orbit  and  fourth  orbit  respectively. 

Variation  of  the  relative  intensity  of  Balmer  and  Paschen  series  lines  of  hydrogen 
with  the  current. — For  the  long  discharge  tube  used,  the  first  Paschen  line  was  found  to 
increase  in  intensity  more  rapidly  than  Ha,  as  the  current  was  increased  from  one- 
ninth  to  one-half  ampere  through  a  section  7  mm  in  diameter. 

INTRODUCTION 

Two  lines  due  to  hydrogen  were  observed  by  Paschen1  at  the 
wave-lengths  18,751  A  and  12,818  A.  According  to  the  Bohr 
theory  these  are  due  to  an  electron  falling  into  the  third  from  the 
fourth  and  fifth  stable  orbits  in  the  hydrogen  atom. 

In  view  of  the  very  low  intensities  of  these  spectral  lines  observed 
by  Paschen,  the  detection  of  a  series  due  to  an  electron  falling  into 
the  fourth  from  orbits  of  greater  quantum  number  has  been  con- 
sidered improbable.  In  fact  the  lines  mentioned  above,  forming 
the  first  two  membeis  of  the  Paschen  series,  were  so  faint  that  in 
order  to  observe  them  Paschen  found  it  necessary  to  set  the  spectro- 
graph  in  the  correct  position  according  to  the  wave-length  predicted 
by  Ritz  in  consequence  of  his  combination  principle. 

By  using  a  very  long  hydrogen  tube  Professor  Wood2  found  it 
possible  to  abolish  the  secondary  spectrum  from  the  central  posi- 
tion of  the  tube,  and  photograph  the  lines  of  the  Balmer  series 
down  to  the  twentieth  member.  From  the  standpoint  of  the  Bohr 
theory,  this  increase  in  the  intensity  of  the  higher  members  of  the 

1  Annalen  der  Physik,  27,  537,  1908. 

'Proceedings  of  the  Royal  Society,  97,  455,  1920;  Philosophical  Magazine,  42, 
729, 1921. 


603606 


RADIATION  OF  HYDROGEN  155 

Balmer  series  might  be  attributed  to  increasing  the  probability  of 
transitions  between  the  orbits  of  higher  quantum  numbers.  That 
being  the  case,  we  should  expect  an  increase  in  the  intensity  of 
lines  of  other  series  which  are  also  due  to  transitions  of  the  electron 
between  orbits  of  higher  quantum  numbers. 

That  this  proved  to  be  the  case,  and  to  a  degree  far  greater 
than  anticipated,  is  the  essential  feature  underlying  the  success 
of  the  present  investigation. 

APPARATUS 

The  hydrogen  tube  of  pyrex  glass,  used  as  the  source,  was  about 
one  meter  in  length.  A  central  portion  25  cm  long  was  viewed 
end  on  through  an  elbow  in  the  tube.  This  portion  of  the  tube 
was  7  mm  in  diameter  (inside  dimension).  This  small-size  tubing 
was  also  used  for  a  distance  of  about  10  cm  on  either  side  of  the 
portion  viewed.  The  remainder  of  the  tube  was  made  of  larger 
diameter  in  order  to  reduce  the  resistance  as  much  as  possible. 
The  electrodes  were  of  thin  aluminum  foil  rolled  into  hollow 
cylinders  8  cm  long  by  2  cm  in  diameter. 

Hydrogen  was  introduced  through  a  capillary  sealed  in  near 
one  electrode.  The  tube  was  exhausted  by  a  Gaede  mercury 
pump,  communicating  with  the  tube  near  the  other  electrode. 
During  observation  the  pump  was  run  continuously,  the  pressure 
depending  upon  the  balance  between  the  pump  and  the  capillary 
intake. 

Alternating  high  potential  was  supplied  by  a  66oo-volt  5- 
kilowatt  transformer  operating  on  a  no- volt,  6o-cycle  primary 
circuit.  The  potential  difference  applied  across  the  tube  was 
varied  by  introducing  resistance  into  the  primary.  The  highest 
current  maintained  through  the  tube  was  a  little  more  than  half 
an  ampere. 

The  dark  space  about  the  electrodes  was  about  3  mm  in  length, 
the  positive  column  occupying  almost  the  entire  length  of  the  tube. 
Striation  appeared  only  in  the  portions  of  the  tube  of  larger  diam- 
eter, the  central  constricted  portion  being  occupied  by  apparently 
continuous  luminosity.  The  secondary  spectrum  was  noticeable 
only  near  the  electrodes.  Throughout  the  greater  part  of  the 


156  FREDERICK  SUMNER  BRACKETT 

tube,  the  B aimer  lines  appeared  with  great  brilliancy  against  a 
practically  black  background  when  the  tube  was  viewed  through 
a  direct-vision  prism. 

The  dispersion  apparatus  was  a  rock-salt  monochromator  of 
the  Wadsworth  type.  Concave  mirrors  of  6o-cm  focal  length  were 
used  for  both  collimator  and  telescope.  The  clear  aperture  of  the 
prism  was  about  4  cm  in  diameter.  Light  only  traversed  the  prism 
once,  the  simple  form  of  apparatus  being  chosen  in  order  to  avoid 
scattered  light.  The  slit  widths  were  about  i  mm. 

The  detecting  apparatus  consisted  of  a  single-junction  vacuum 
thermo-couple,  of  the  type  constructed  and  previously  used  by 
Professor  Pfund  for  measurement  of  stellar  radiation.  This  was 
connected  in  series  with  a  d'Arsonval  galvonometer  of  sensibility 
about  5Xio~10. 

A  scale-distance  of  three  meters  was  used,  giving  altogether 
an  arrangement  of  extreme  sensibility. 

The  light  from  the  second  slit  was  concentrated  upon  the  black- 
ened strip  of  the  thermo-junction  by  means  of  a  short-focus  con- 
cave mirror.  Both  mirror  and  thermo-junction  were  protected 
by  an  asbestos  housing.  The  leads  to  the  galvanometer  were 
carried  through  a  metal  conduit,  grounded  to  prevent  electro- 
static effects.  The  galvanometer  case,  posts,  etc.,  were  heavily 
covered  with  cotton  batting.  The  stability  of  this  arrangement 
proved  very  satisfactory,  deflections  being  reliable  to  o.i  mm. 

RESULTS 

Part  I.  Distribution  of  intensity. — Figure  i  shows  the  distribu- 
tion of  intensity  of  radiation  due  to  hydrogen  in  the  infra-red 
between  wave-lengths  0.5  ju  and  4.5  ju. 

In  this  diagram  intensities  have  been  plotted  as  the  ordinates 
measured  in  millimeters  of  deflection  of  the  galvanometer.  It  has 
been  shown  that  intensities  are  proportional  to  galvanometer 
deflections  for  this  thermo-couple  for  small  deflections  such  as  are 
obtained  here.  The  abscissae  are  simply  micrometer  turns  of  the 
monochromator.  The  dispersion-curve  based  on  five  known 
points  of  the  monochromator  is  shown  superposed.  Its  ordinates 


RADIATION  OF  HYDROGEN 


are  wave-lengths  in  microns  indicated  on  the  right.     In  order  to 
read  the  wave-length  of  any  point  on  the  intensity-curve  it  is 


FIG.  i 


merely  necessary  to  find  the  point  of  the  dispersion-curve  having 
the  same  abscissa  and  read  its  ordinate  at  the  right. 


FREDERICK  SUMNER  BRACKETT 


The  maximum  occurring  at  4.05=^.03  p  and  the  second  one  at 
2.63^.02  jii  are  the  first  two  members  of  a  new  series  predicted 
from  the  Bohr  theory  by  the  formula 

i/X=  109,677.7  (i/42-i/w2);  m  =  $.6. 

That  is,  they  are  attributed  to  an  electron  falling  into  the  fourth 
from  the  fifth  and  sixth  stable  orbits  of  the  hydrogen  atom  accord- 
ing to  Bohr's  model. 

The  largest  maximum  occurring  at  i  .88  fj.  is  the  first  line  of  the 
Paschen  series.  It  will  be  noted  that  it  has  an  intensity  greater 
than  Ha  (the  last  maximum  on  the  left)  in  the  ratio  of  about  4 
to  3.  The  next  four  maxima  are  the  next  four  members  of  the 
Paschen  series. 

The  identity  of  the  succeeding  maxima  is  uncertain.  Other 
lines  are  certainly  present  which  do  not  belong  to  the  Paschen 
series.  The  second  maximum  is  probably  Pf . 

These  lines  of  the  Paschen  series  are  predicted  from  the  Bohr 
theory  by  the  formula 

i/X  =  109,677.7  (i/32-i/w2);  m  =  4,  5,  6,  7,  8,  (9),  10. 


Line 

Observed  Wave- 
Length 

Calculated  Wave- 
Length 

Pa.. 

(l.88/i) 

I   87?  u 

PS 

(l    28  M) 

1  .  282  fj. 

Pv            

I    00=*=    OI  U 

I   OQ4  u 

P5  

I  .OI=*=  .OI  fj. 

1  .005  fj. 

Pe  

O.QS^  .OI  U 

O.O<?  u 

The  dispersion-curve  from  which  the  wave-lengths  have  been 
determined  is  based  upon  five  known  points:  4.4  /j.  and  2.7  n  of 
the  Bunsen  flame  (shown  by  dotted  lines — scale  reduced  100  times) 
and  the  three  known  hydrogen  lines  Pa,  P/3,  and  Ha.  The  values 
thus  obtained  should  be  quite  satisfactory  for  purposes  of  identi- 
fication, but  of  course  have  no  great  value  from  the  standpoint  of 
accurate  wave-length  measurement. 

In  view  of  the  great  intensity  of  the  Paschen  lines  it  is  not 
surprising  that  many  lines  were  readily  observed  which  under 
ordinary  conditions  of  excitation  would  not  be  detected.  The 


RADIATION  OF  HYDROGEN 


159 


readings  shown  on  Figure  i  were  taken  in  sequence,  without  setting 
upon  known  wave-lengths.  The  identity  of  the  maxima  was  not 
realized  until  the  dispersion-curve  was  later  plotted. 

Part  II.  Variation  of  intensity  with  current. — As  it  was  noticed 
that  the  appearance  of  the  tube  changed  decidedly  with  change 
in  current,  a  set  of  intensity  readings  was  taken  on  the  first  lines 
of  three  series — the  Balmer,  the  Paschen,  and  the  new  series,  when 
the  current  through  the  tube  was  varied  from  one-sixth  of  an 
ampere  to  over  one-half  an  ampere.  The  curves  obtained  are 
shown  in  Figure  2. 


10  If  jt         Ante 


FIG.  2 


The  ordinates  are  intensities  in  millimeter  deflections  of  the 
galvanometer,  and  the  abscissae  are  current  strengths  through 
the  primary  of  the  transformer.  The  current  through  the  tube 
is  found  with  sufficient  accuracy  by  dividing  by  60.  Readings  on 
a  of  the  new  series  are  not  shown  for  currents  greater  than  20 
amperes  primary,  one-third  ampere  secondary,  as  radiation  from 
the  glass  tube  itself  rendered  them  uncertain.  No  such  effect  was 
observed  for  lower  currents  or  wave-lengths  less  than  3.5  p.  As  a 
further  precaution  the  tube  was  run  only  during  the  time  of  actual 
reading. 


i6o  FREDERICK  SUMNER  BRACKETT 

From  this  diagram,  Figure  2,  it  will  be  noticed  that  although  all 
three  lines  increase  in  intensity  with  increasing  current,  Pa  increases 
by  far  the  most  rapidly.  Further  readings  (dotted  portion  of  the 
curve)  showed  that  at  currents  less  than  7  amperes  primary  (about 
one-ninth  ampere  secondary)  Ha  was  more  intense  than  Pa. 

At  a  current  of  23  amperes  through  the  primary  we  have  the 
ratio  of  the  intensity  of  Pa  to  Ha  a  little  more  than  4  to  3.  Accord- 
ing to  the  Bohr  theory  the  energy  lost  by  an  electron  undergoing 
transition  from  the  fourth  to  the  third  orbit  of  the  hydrogen  atom 
will  be 

WPa=(i/32-i/4')  Nh  = 


while  that  lost  in  transition  from  the  third  to  the  second  orbit 
would  be 

WHa=(i/22-i/32)  Nh= 


So  the  energy  given  out  by  an  electron  in  transition  from  the 
fourth  to  the  third  orbit  is  only  seven-twentieths  of  that  given  out 
by  an  electron  falling  from  the  third  to  the  second  orbit.  Hence, 
in  order  to  have  Pa  more  intense  than  Ha  in  the  ratio  4:3,  there  must 
be  more  atoms  radiating  Pa  than  Ha  in  the  ratio  of 


In  view  of  the  greater  stability  of  the  orbits  of  smaller  quantum 
number  and  taking  into  account  the  principle  of  selection,  we  see 
that  this  is  incompatible  with  what  would  be  expected  if  radiation 
were  resulting  only  from  recombination  of  the  atom  and  electron 
after  ionization.  We  must  therefore  conclude  that  to  a  large  extent 
radiation  in  such  a  long  hydrogen  tube  arises  from  inelastic  collision 
without  ionization.  In  such  a  case  we  may  have  an  abnormal 
concentration  of  energy  in  certain  wave-lengths  which  would  not 
be  the  case  for  recombination  after  ionization,  inasmuch  as  the 
probability  of  an  electron  stopping  in  an  orbit  of  high  quantum 
number  is  much  greater,  where  it  is  simply  ejected  to  that  orbit  or 
one  of  slightly  greater  quantum  number,  than  in  the  case  where  it 


RADIATION  OF  HYDROGEN  161 

is  returning  from  oo  .  This  no  doubt  explains  to  a  large  extent  the 
peculiar  characteristics  of  the  "long  hydrogen  tube,"  both  in  regard 
to  the  unusual  intensity  of  the  infra-red  lines  and  also  the  higher 
members  of  the  B  aimer  series. 

All  atoms  which  contribute  to  the  radiation  of  the  first  Paschen 
line  are  left  necessarily  with  the  electron  in  the  third  orbit,  whence 
it  must  proceed  either  to  the  second  or  the  first  orbit  unless  it  is 
ejected  to  some  orbit  of  greater  quantum  number  by  inelastic 
collision.  Since  considerably  less  than  one-fourth  of  these  atoms 
contribute  to  the  radiation  of  Ha,  we  must  conclude  either  that 
the  second  member  of  the  Lyman  series  is  radiated  with  great 
intensity,  or  that  there  must  be  multiple  collisions  to  a  large  extent 
in  such  a  tube. 

It  should  be  noticed  that  the  higher  members  of  the  Paschen 
series  occur  in  a  region  readily  studied  by  photographic  methods, 
plates  hypersensitized  by  means  of  dicyanin  being  sensitive  to  i.o  p. 
This  work  will  be  carried  out  in  the  near  future. 

CONCLUSION 

1.  The  first  two  lines  of  a  new  series  have  been  observed  at 
wave-lengths  4.05=*=  .03  ju  and  2.63=1=  .02  /*,  due,  according  to  Bohr's 
theory,  to  an  electron  falling  into  the  fourth  from  the  fifth  and  sixth 
rings  of  the  hydrogen  atom. 

2.  Three  and  probably  four  additional  members  of  the  Paschen 
series  have  been  observed. 

3.  The  first  Paschen  line  is  more  intense  than  Ha  in  the  ratio 
4:3  under  the  conditions  prevailing  in  the  long  tube  for  great  current 
densities. 

In  this  work  I  have  been  much  indebted  to  Dr.  Pfund,  who 
proposed  the  problem  and  constructed  the  thermo-junction,  the 
remarkable  sensibility  of  which  rendered  the  work  possible. 

It  gives  me  great  pleasure  to  express  my  appreciation  to  him, 
to  Professor  Wood  for  his  interest  and  many  suggestions,  and  to 
Dr.  Ames  for  his  generous  support. 

JOHNS  HOPKINS  UNIVERSITY 
June  1922 


BIOGRAPHICAL  NOTE 

Frederick  Summer  Brackett,  son  of  Frank  Parkhurst  and  Lucretia 
(Burdick)  Brackett,  was  born  August  i,  1896,  in  Claremont,  California.  His 
preliminary  education  was  obtained  in  the  Claremont  public  schools.  He 
graduated  from  the  high  school  in  1910,  entering  Pomona  College  the  following 
fall,  where  he  pursued  the  general  course,  majoring  in  physics  and  mathe- 
matics. He  was  elected  to  Phi  Beta  Kappa  in  the  spring  of  his  Junior  year. 
He  graduated  cum  laude  in  February,  1918,  receiving  the  B.A.  degree  in  absentia. 

He  was  laboratory  assistant  in  the  optical  section  of  the  Bureau  of  Standards 
for  the  year  1918-19,  at  the  same  time  pursuing  courses  in  advanced  physics 
and  mathematics  given  by  Professor  Ames.  He  was  a  solar  observer  on  the 
staff  of  Mt.  Wilson  Solar  Observatory  during  1919-20,  the  published  results  of 
his  research  being  An  Examination  of  the  Infra-Red  Spectrum  of  the  Sun  A.  8goo 
to  X  9900  A°. 

He  was  appointed  instructor  in  physics  at  the  Johns  Hopkins  University 
in  the- fall  of  1920.  While  there  during  the  following  two  years  he  pursued 
graduate  courses  in  physics,  mathematical  physics,  and  dynamical  geology  under 
Professors  Ames,  Murnaghan,  and  Reid. 

He  was  an  assistant  physicist  at  the  Bureau  of  Standards  during  the  summer 
of  1920,  being  retained  through  the  winter  in  a  consulting  capacity. 


OCT 


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